How can i determine degree of trigonometric polynomial? I know the highest power in a univariate polynomial is known as its degree, but what is degree of trigonometric polynomial? Please help me
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$\begingroup$To determine the degree of an algebraic polynomial, we bring to to the canonical form $$c_0+c_1 x+c_2 x^2+ \dots +c_nx^n\tag{1}$$ with $c_n$ not equal to $0$. The number $n$ is the degree of this polynomial.
To determine the degree of an trigonometric polynomial, we also bring to to the canonical form $$a_0+ a_1 \cos x+b_1\sin x + a_2 \cos 2x+b_2 \sin 2x + \dots + a_n\cos nx+b_n \sin nx \tag{2}$$ with at least one of $a_n,b_n$ not equal to zero. The number $n$ is the degree of this trigonometric polynomial.
Alternatively, you can write (2) in complex form, as a sum of $c_ke^{ikx}$, $c_k \in\mathbb C$. Then the degree is the maximum of $|k|$ among the terms with $c_k\ne 0$. This is closer to (1), especially because $e^{ikx}$ is $e^{ix}$ raised to power $k$.
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